The Painlevé Property and Hirota's Method

On etudie la relation entre la propriete de Painleve et la methode de Hirota pour calculer des solutions N-solitons pour differentes equations d'evolution non lineaires

[1]  M. Crum ASSOCIATED STURM-LIOUVILLE SYSTEMS , 1999, physics/9908019.

[2]  Sophie Kowalevski,et al.  Sur le probleme de la rotation d'un corps solide autour d'un point fixe , 1889 .

[3]  C. Newman Inequalities for Ising models and field theories which obey the Lee-Yang Theorem , 1975 .

[4]  J. Weiss THE PAINLEVE PROPERTY FOR PARTIAL DIFFERENTIAL EQUATIONS. II. BACKLUND TRANSFORMATION, LAX PAIRS, AND THE SCHWARZIAN DERIVATIVE , 1983 .

[5]  Hugo D. Wahlquist,et al.  Backlund transformation for solutions of the Korteweg-de Vries equation , 1973 .

[6]  M. Ablowitz,et al.  Nonlinear evolution equations and ordinary differential equations of painlevè type , 1978 .

[7]  V. Zakharov,et al.  Korteweg-de Vries equation: A completely integrable Hamiltonian system , 1971 .

[8]  J. Gibbon,et al.  A modified regularized long-wave equation with an exact two-soliton solution , 1976 .

[9]  Ryogo Hirota,et al.  Exact Solution of the Sine-Gordon Equation for Multiple Collisions of Solitons , 1972 .

[10]  Junkichi Satsuma,et al.  N-Soliton Solution of the Two-Dimensional Korteweg-deVries Equation , 1976 .

[11]  D. J. Benney Some Properties of Long Nonlinear Waves , 1973 .

[12]  Ryogo Hirota,et al.  Exact Solution of the Modified Korteweg-de Vries Equation for Multiple Collisions of Solitons , 1972 .

[13]  Jürgen Moser,et al.  On a class of polynomials connected with the Korteweg-deVries equation , 1978 .

[14]  F. Vivaldi,et al.  Integrable Hamiltonian Systems and the Painleve Property , 1982 .

[15]  G. Wilson,et al.  The affine lie algebra C(1)2 and an equation of Hirota and Satsuma , 1982 .

[16]  M. Tabor,et al.  The Painlevé property for partial differential equations , 1983 .

[17]  H. McKean,et al.  Rational and elliptic solutions of the korteweg‐de vries equation and a related many‐body problem , 1977 .

[18]  P. Olver,et al.  The Connection between Partial Differential Equations Soluble by Inverse Scattering and Ordinary Differential Equations of Painlevé Type , 1983 .

[19]  J. C. Eilbeck,et al.  Exact Multisoliton Solutions of the Self-Induced Transparency and Sine-Gordon Equations , 1973 .

[20]  D. V. Choodnovsky,et al.  Pole expansions of nonlinear partial differential equations , 1977 .

[21]  M. Ablowitz,et al.  A connection between nonlinear evolution equations and ordinary differential equations of P‐type. II , 1980 .

[22]  M. Tabor,et al.  Painlevé property and multicomponent isospectral deformation equations , 1983 .

[23]  Mark J. Ablowitz,et al.  Exact Linearization of a Painlevé Transcendent , 1977 .

[24]  J. Weiss,et al.  The sine‐Gordon equations: Complete and partial integrability , 1984 .

[25]  Ryogo Hirota,et al.  Exact N‐soliton solutions of the wave equation of long waves in shallow‐water and in nonlinear lattices , 1973 .

[26]  R. Hirota Exact solution of the Korteweg-deVries equation for multiple collision of solitons , 1971 .

[27]  R. Hirota,et al.  Theoretical and experimental studies of lattice solitons in nonlinear lumped networks , 1973 .

[28]  J. Satsuma Solitons and Rational Solutions of Nonlinear Evolution Equations (Theory of Nonlinear Waves) , 1978 .

[29]  M. Tabor,et al.  Analytic structure of the Henon–Heiles Hamiltonian in integrable and nonintegrable regimes , 1982 .

[30]  R. Hirota,et al.  N-Soliton Solutions of Model Equations for Shallow Water Waves , 1976 .

[31]  R. Hirota,et al.  Soliton solutions of a coupled Korteweg-de Vries equation , 1981 .

[32]  Allan P. Fordy,et al.  On the integrability of a system of coupled KdV equations , 1982 .

[33]  M. Ablowitz,et al.  Nonlinear-evolution equations of physical significance , 1973 .

[34]  Ryogo Hirota,et al.  A New Form of Bäcklund Transformations and Its Relation to the Inverse Scattering Problem , 1974 .

[35]  C. S. Gardner,et al.  Method for solving the Korteweg-deVries equation , 1967 .